XII
If we turn back from Nature-feeling become form to Nature-knowledge become system, we know God or the gods as the origin of the images by which the intellect seeks to make the world-around comprehensible to itself. Goethe once remarked (to Riemer): “The Reason is as old as the World; even the child has reason. But it is not applied in all times in the same way or to the same objects. The earlier centuries had their ideas in intuitions of the fancy, but ours bring them into notions. The great views of Life were brought into shapes, into Gods; to-day they are brought into notions. Then the productive force was greater, now the destructive force or art of separation.” The strong religiousness of Newton’s mechanics[[515]] and the almost complete atheism of the formulations of modern dynamics are of like colour, positive and negative of the same primary feeling. A physical system of necessity has all the characters of the soul to whose world-form it belongs. The Deism of the Baroque belongs with its dynamics and its analytical geometry; its three basic principles, God, Freedom and Immortality, are in the language of mechanics the principles of inertia (Galileo), least action (D’Alembert) and the conservation of energy (J. R. Mayer).
That which nowadays we call quite generally physics is in reality an artifact of the Baroque. At this stage the reader will not feel it as paradoxical to associate the mode of representation which rests on the assumption of distant forces and the (wholly un-Classical and anything but naïve) idea of action-at-a-distance, attraction and repulsion of masses, specially with the Jesuit style of architecture founded by Vignola, and to call it accordingly the Jesuit style of physics; and I would likewise call the Infinitesimal Calculus, which of necessity came into being just when and where it did, the Jesuit style of mathematic. Within this style, a working hypothesis that deepens the technique of experimentation is “correct”; for Loyola’s concern, like Newton’s, was not description of Nature but method.
Western physics is by its inward form dogmatic and not ritualistic (kultisch). Its content is the dogma of Force as identical with space and distance, the theory of the mechanical Act (as against the mechanical Posture) in space. Consequently its tendency is persistently to overcome the apparent. Beginning with a still quite Apollinian-sensuous classification of physics into the physics of the eye (optics), of the ear (acoustics) and of the skin-sense (heat), it by degrees eliminated all sense-impressions and replaced them by abstract systems of relations; thus, under the influence of ideas concerning dynamical motion in an æther, radiant heat is nowadays dealt with under the heading of “optics,” a word which has ceased to have anything to do with the eye.
“Force” is a mythical quantity, which does not arise out of scientific experimentation but, on the contrary, defines the structure thereof a priori. It is only the Faustian conception of Nature that instead of a magnet thinks of a magnetism whose field of force includes a piece of iron, and instead of luminous bodies thinks of radiant energy, and that imagines personifications like “electricity,” “temperature” and “radioactivity.”[[516]]
That this “force” or “energy” is really a numen stiffened into a concept (and in nowise the result of scientific experience) is shown by the often overlooked fact that the basic principle known as the First Law of Thermodynamics[[517]] says nothing whatever about the nature of energy, and it is properly speaking an incorrect (though psychologically most significant) assumption that the idea of the “Conservation of Energy” is fixed in it. Experimental measurement can in the nature of things only establish a number, which number we have (significantly, again) named work. But the dynamical cast of our thought demanded that this should be conceived as a difference of energy, although the absolute value of energy is only a figment and can never be rendered by a definite number. There always remains, therefore, an undefined additive constant, as we call it; in other words, we always strive to maintain the image of an energy that our inner eye has formed, although actual scientific practice is not concerned with it.
This being the provenance of the force-concept, it follows that we can no more define it than we can define those other un-Classical words Will and Space. There remains always a felt and intuitively-perceived remainder which makes every personal definition an almost religious creed of its author. Every Baroque scientist in this matter has his personal inner experience which he is trying to clothe in words. Goethe, for instance, could never have defined his idea of a world-force, but to himself it was a certainty. Kant called force the phenomenon of an ent-in-itself: “we know substance in space, the body, only through forces.” Laplace called it an unknown of which the workings are all that we know, and Newton imagined immaterial forces at a distance. Leibniz spoke of Vis viva as a quantum which together with matter formed the unit that he called the monad, and Descartes, with certain thinkers of the 18th Century, was equally unwilling to draw fundamental distinctions between motion and the moved. Beside potentia, virtus, impetus we find even in Gothic times peri-phrases such as conatus and nisus, in which the force and the releasing cause are obviously not separated. We can, indeed, quite well differentiate between Catholic, Protestant and Atheistic notions of force. But Spinoza, a Jew and therefore, spiritually, a member of the Magian Culture, could not absorb the Faustian force-concept at all, and it has no place in his system.[[518]] And it is an astounding proof of the secret power of root-ideas that Heinrich Hertz, the only Jew amongst the great physicists of the recent past, was also the only one of them who tried to resolve the dilemma of mechanics by eliminating the idea of force.
The force-dogma is the one and only theme of Faustian physics. That branch of science which under the name of Statics has been passed from system to system and century to century is a fiction. “Modern Statics” is in the same position as “arithmetic” and “geometry,” which, if the literal and original senses of the words be kept to, are void of meaning in modern analysis, empty names bequeathed by Classical science and only preserved because our reverence for all things Classical has hitherto debarred us from getting rid of them or even recognizing their hollowness. There is no Western statics—that is, no interpretation of mechanical facts that is natural to the Western spirit bases itself on the ideas of form and substance, or even, for that matter, on the ideas of space and mass otherwise than in connexion with those of time and force.[[519]] The reader can test this in any department that he pleases. Even “temperature,” which of all our physical magnitudes has the most plausible look of being static, Classical and passive, only falls into its place in our system when it is brought into a force-picture, viz., the picture of a quantity of heat made up of ultra-swift subtle irregular motions of the atoms of a body, with temperature as the mean vis viva of these atoms.
The Late Renaissance imagined that it had revived the Archimedean physics just as it believed that it was continuing the Classical sculpture. But in the one case as in the other it was merely preparing for the forms of the Baroque, and doing so out of the spirit of the Gothic. To this Statics belongs the picture-subject as it is in Mantegna’s work and also in that of Signorelli, whose line and attitude later generations regarded as stiff and cold. With Leonardo, dynamics begins and in Rubens the movement of swelling bodies is already at a maximum.
As late as 1629 the spirit of Renaissance physics appears in the theory of magnetism formulated by the Jesuit Nicolaus Cabeo. Conceived in the mould of an Aristotelian idea of the world, it was (like Palladio’s work on architecture) foredoomed to lead to nothing—not because it was “wrong” in itself but because it was in contradiction with the Faustian Nature-feeling which, freed from Magian leading-strings by the thinkers and researchers of the 14th Century, now required forms of its very own for the expression of its world-knowledge. Cabeo avoided the notions of force and mass and confined himself to the Classical concepts of form and substance—in other words, he went back from the architecture of Michelangelo’s last phase and of Vignola to that of Michelozzo and Raphael—and the system which he formed was complete and self-contained but without importance for the future. A magnetism conceived as a state of individual bodies and not as a force in unbounded space was incapable of symbolically satisfying the inner eye of Faustian man. What we need is a theory of the Far, not one of the Near. Newton’s mathematical-mechanical principles required to be made explicit as a dynamics pure and entire, and this another Jesuit, Boscovich,[[520]] was the first to achieve in 1758.
Even Galileo was still under the influence of the Renaissance feeling, to which the opposition of force and mass, that was to produce, in architecture and painting and music alike the element of grand movement, was something strange and uncomfortable. He therefore limited the idea of force to contact-force (impact) and his formulation did not go beyond conservation of momentum (quantity of motion). He held fast to mere moved-ness and fought shy of any passion of space, and it was left to Leibniz to develop—first in the course of controversy and then positively by the application of his mathematical discoveries—the idea of genuine free and directional forces (living force, activum thema). The notion of conservation of momentum then gave way to that of conservation of living forces, as quantitative number gave way to functional number.
The concept of mass, too, did not become definite until somewhat later. In Galileo and Kepler its place is occupied by volume, and it was Newton who distinctly conceived it as functional—the world as function of God. That mass (defined nowadays as the constant relation between force and acceleration in respect of a system of material points) should have no proportionate relation whatever to volume was, in spite of the evidence of the planets, a conclusion inacceptable to Renaissance feeling.
But, even so, Galileo was forced to inquire into the causes of motion. In a genuine Statics, working only with the notions of material and form, this question would have had no meaning. For Archimedes displacement was a matter of insignificance compared with form, which was the essence of all corporeal existence; for, if space be Nonent, what efficient can there be external to the body concerned? Things are not functions of motion, but they move themselves. Newton it was who first got completely away from Renaissance feeling and formed the notion of distant forces, the attraction and repulsion of bodies across space itself. Distance is already in itself a force. The very idea of it is so free from all sense-perceptible content that Newton himself felt uncomfortable with it—in fact it mastered him and not he it. It was the spirit of Baroque itself, with its bent towards infinite space, that had evoked this contrapuntal and utterly un-plastic notion. And in it withal there was a contradiction. To this day no one has produced an adequate definition of these forces-at-a-distance. No one has ever yet understood what centrifugal force really is. Is the force of the earth rotating on its axis the cause of this motion or vice versa? Or are the two identical? Is such a cause, considered per se, a force or another motion? What is the difference between force and motion? Suppose the alterations in the planetary system to be workings of a centrifugal force; that being so, the bodies ought to be slung out of their path [tangentially], and as in fact they are not so, we must assume a centrifugal force as well. What do all these words mean? It is just the impossibility of arriving at order and clarity here that led Hertz to do away with the force-notion altogether and (by highly artificial assumptions of rigid couplings between positions and velocities) to reduce his system of mechanics to the principle of contact (impact). But this merely conceals and does not remove the perplexities, which are of intrinsically Faustian character and rooted in the very essence of dynamics. “Can we speak of forces which owe their origin to motion?” Certainly not; but can we get rid of primary notions that are inborn in the Western spirit though indefinable? Hertz himself made no attempt to apply his system practically.
This symbolic difficulty of modern mechanics is in no way removed by the potential theory that was founded by Faraday when the centre of gravity of physical thought had passed from the dynamics of matter to the electrodynamics of the æther. The famous experimenter, who was a visionary through and through—alone amongst the modern masters of physics he was not a mathematician—observed in 1846: “I assume nothing to be true in any part of space (whether this be empty as is commonly said, or filled with matter) except forces and the lines in which they are exercised.” Here, plain enough, is the directional tendency with its intimately organic and historic content, the tendency in the knower to live the process of his knowing. Here Faraday is metaphysically at one with Newton, whose forces-at-a-distance point to a mythic background that the devout physicist declined to examine. The possible alternative way of reaching an unequivocal definition of force—viz., that which starts from World and not God, from the object and not the subject of natural motion-state—was leading at the very same time to the formulation of the concept of Energy. Now, this concept represents, as distinct from that of force, a quantum of directedness and not a direction, and is in so far akin to Leibniz’s conception of “living force” unalterable in quantity. It will not escape notice that essential features of the mass-concept have been taken over here; indeed, even the bizarre notion of an atomic structure of energy has been seriously discussed.
This rearrangement of the basic words has not, however, altered the feeling that a world-force with its substratum does exist. The motion-problem is as insoluble as ever. All that has happened on the way from Newton to Faraday—or from Berkeley to Mill—is that the religious deed-idea has been replaced by the irreligious work-idea.[[521]] In the Nature-picture of Bruno, Newton and Goethe something divine is working itself out in acts, in that of modern physics Nature is doing work; for every “process” within the meaning of the First Law of Thermodynamics is or should be measurable by the expenditure of energy to which a quantity of work corresponds in the form of “bound energy.”
Naturally, therefore, we find the decisive discovery of J. R. Mayer coinciding in time with the birth of the Socialist theory. Even economic systems wield the same concepts; the value-problem has been in relation with quantity of work[[522]]] ever since Adam Smith, who vis-à-vis Quesney and Turgot marks the change from an organic to a mechanical structure of the economic field. The “work” which is the foundation of modern economic theory has purely dynamic meaning, and phrases could be found in the language of economists which correspond exactly to the physical propositions of conservation of energy, entropy and least action.
If, then, we review the successive stages through which the central idea of force has passed since its birth in the Baroque, and its intimate relations with the form-worlds of the great arts and of mathematics, we find that (1) in the 17th Century (Galileo, Newton, Leibniz) it is pictorially formed and in unison with the great art of oil-painting that died out about 1630; (2) in the 18th Century (the “classical” mechanics of Laplace and Lagrange) it acquires the abstract character of the fugue-style and is in unison with Bach; and (3) with the Culture at its end and the civilized intelligence victorious over the spiritual, it appears in the domain of pure analysis, and in particular in the theory of functions of several complex variables, without which it is, in its most modern form, scarcely understandable.